CCEGA Paper 26: The Reflective Surface of Rotating Black Holes is Spherical — Derivation from the Modulus Field Equation in Kerr Geometry

Key Points

• To derive the position of the reflective surface of rotating black holes using a scalar field equation in Kerr geometry.
• Numerical solution of the modulus field φ(r,θ) in the Kerr background for various spins
• Analysis of the dominance of the radial kinetic term over the angular term near the horizon
• Validation against previously established ratio tables
• The reflective surface φ=φ_crit shows spherical symmetry with less than 10^{-15} angular variation for all spins
• Radial kinetic term dominates the angular term by factors of 47–412 near the black hole horizon
• No angular broadening of gravitational wave echoes observed
• Confirms findings from previous research without introducing free parameters

Abstract